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Project 1: Fourier coefficients Due: /////////////Wednesday,////////////September//8 Tuesday, September 14
 

Summary: Project 1: Fourier coefficients
Due: /////////////Wednesday,////////////September//8 Tuesday, September 14
One reason to be able to compute trigonometric integrals is for Fourier analysis; given a function,
we can try to approximate it as a sum of functions like sin(mx) and cos(nx).
If f (x) and g(x) are two functions, define the number
f (x), g(x) =
1


-
f (x)g(x) dx.
Throughout this problem, assume that m and n are integers.
1. Before we start, we'll need to verify the following identities from the text (page 585):
sin(mx) sin(nx) =
1
2
(cos((m - n)x) - cos((m + n)x)) (1)
sin(mx) cos(nx) =
1
2

  

Source: Achter, Jeff - Department of Mathematics, Colorado State University

 

Collections: Environmental Sciences and Ecology; Mathematics